If you want to use a multimeter to test from one end, you could build a female connection pigtail for one end. Then, one by one, short the wires coming off the pigtail. Attach 1 to 2, then 1 to 3, then 1 to 4 etc. Then, at the other end of things, use your continuity tester by touching 1 and 2, 1 and 3, 1 and 4 etc
You'll have to run back and forth each time to disconnect and reconnect each pair, but it should let you track down a possible break somewhere. Although honestly, the first thing I'd do is to cut off the ends of the existing cable and re-crimp a new connector. For me, any problems have been related to my crimping and not a broken wire in the middle of things.